For the time being my daughter thinks everything in English is 'cool'. So we started math in English, except it's not 'just' math in English.

Apparently the program is totally, totally different from the Belgian one. I bought Math Mammoth, the Blue Series, which means we can work per topic and not by grade. The advantage sure is we can progress faster on the topics she likes and take it easy on the topics that won't work (like fractions). We also have to review everything, because even the approach/teaching method itself is different most of the time and some stuff is new.

Anyway, there are a lot of things that we, Belgians, don't learn in elementary school (1-6th grade). If I have a correct overview, new to us is statistics and probability, and the overall level reached in the American 6th grade would be the level in our 8th grade with some things never even learned depending on what you study after 6th grade. Statistics and probability (even the basics) are also only for the happy few in the most 'mathy' directions. I must say I'm impressed.

So what's my question? Could someone please explain the difference between K-6 and K-8 curricula? Is K-8 more elaborate, does it contain more exercises or does it offer more than that? And what afterwards? I read there's something like pre-algebra. Maybe that's the difference between K-6 and K-8?

I also don't understand what pre-algebra is. I have seen exercises in 6th grade that - to a Belgian - would qualify as algebra.

I'd be happy with the answer to those questions, but if someone has some spare time left, I'm also wondering what happens after 8th grade. I've read there's 2 years of algebra, 1 of geometry/trigonometry and 1 I can't remember.

From what I remember (and it differs quite a bit from curriculum to curriculum) pre-Algebra is basically just simple Algebra--an introduction to working with variables, solving for x, and things of that nature. No huge differences, except you don't get into more complex things like the quadratic formula until you hit Algebra.

I'm not too sure about K-6 vs. K-8, but I know that after year 8, math topics generally go like this:

Unlesss you're going the more classical route, a full course on geometry is in my opinion unnecessary, since there's enough geometry mixed into Algebra and everything that comes after for you to make do. Similarly, Algebra II and the early parts of Calculus contain enough Trig / Pre-Calc for you to skip doing those as separate courses unless you really happen to enjoy the material. This could of course vary based on course material, but I personally went straight from elementary math (assorted textbooks, drill practice) to Algebra I and II (Saxon) and from there straight to Calculus I, II, and III (college textbooks for I and II, took a community college course for III). I did take Discrete Math and Statistics as separate courses, but those were college-level courses with advanced material. What you're probably talking about is simple probability, things like "If you have 6 red buttons and 7 blue buttons and randomly pick two, what are the chances both are red?", or maybe how to read a graph.

You might want to call it 'simple probability', but over here the majority of students never know what that is. At best, they learn about it starting in 9th grade, but only if they are in heavy math directions.

It's all really confusing to me. I don't have problems with the matter itself, but we're just not used to this order, which means -although my daughter is supposed to be in 5th grade - we have to start over from the beginning. And I want to get it right. I'm sick of buying books that go unused!

So, if pre-algebra is nothing more than solving for x, you could skip pre-algebra? If your kid 'gets' it, of course. Same thing apparently for pre-calculus.

About geometry, you would only take that course if you would need it later on for college? I guess American children aren't all studying the same things at the same level till they're 18? Our children get to choose after 8th grade (or 6th grade). They might just as well choose a profession for which they really don't need advanced math.

Here, Advanced Math is another course you can take between Algebra II and Calculus. Is that what you meant, or did you mean something else? I went partly through an Advanced Math textbook, found it to be heavily trig and not particularly fun, so I skipped that and went to Calculus.

This is from the high school graduation requirements for my state (Missouri):

Missouri high school graduates must earn at least three units selected to ensure that students have strong problem-solving skills and a foundation in the mathematical concepts of number sense, geometry and spatial sense, measurement, data analysis, statistics, patterns and relationships, algebraic thinking, mathematical systems, number theory, and discrete topics.

Note that it doesn't say anything about specifically taking a geometry course, so if you've managed to absorb enough from other courses, you can avoid geometry as a separate subject. But you're theoretically expected to understand a lot of material overall. Personally, math is one of my strong points, so about the only two things I had trouble understanding on the way through high school math were functions and exponential growth and decay. For some reason those took me a little while to wrap my head around. Calculus I and especially II were also nasty to try to learn just from a textbook - could have saved myself a lot of pain and suffering if I'd just taken them as community college courses, like I did for Calc III.

Pre-Algebra apparently spans a lot more than solving for x, but you cover all this same material earlier on in Algebra I, so it really makes no difference whether you do Pre-Algebra and then skip parts of Algebra I, or just do all of Algebra I - except the latter method might be a bit more efficient.
http://en.wikipedia.org/wiki/Pre-algebra

Honestly, I wouldn't worry about this all -too- much. Just get some decent textbooks to work from (I like Saxon up through the end of high school) and work at whatever speed you feel comfortable. If you homeschool year-round instead of following the typical school semester schedule, it's extremely hard to fall behind - you'd have to be studying less than 2-3 hours per day (for all subjects, not just math) and not trying very hard when you were studying.